Direct pressure field reconstruction using boundary-independent shortest-path integration

Pressure measurement is of great importance in fluid mechanics and the direct reconstruction of the pressure field by integrating the pressure gradient fields has been realized. However, most of the current algorithms initiate the integration at the boundary where the pressure gradient measurement is often unreliable. In this study, we introduce the boundary-independent shortest-path (BISP) integration algorithm for planar pressure reconstruction whereby the integration starts at the inner domain of the pressure gradient field and grows outward toward the boundaries. The pressure at any given point is calculated by averaging over millions of shortest path line integrations originating from already developed points. The algorithm is first validated using a direct numerical simulation (DNS) forced isotropic turbulence dataset. Further, we demonstrate the ability to reconstruct pressure fields containing inner voids of arbitrary sizes and shapes. We also show the applicability of this algorithm in experimental datasets by reconstructing the pressure field around a bacteria streamer grown on an oil droplet. Overall, this algorithm can reconstruct pressure fields with high accuracy without propagation of boundary errors or any dependency on the boundary values.